On the eve of a special function in view of ‘National Integration’, seven participants – $\text{A, B, C, D, E, F}$ and $\text{G}$, are to be accommodated in two rooms, each room having a capacity of four persons only. For the allocation, the following conditions must be considered.
- $\text{A}$, a Gujarati, also speak Tamil and Bengali.
- $\text{B}$ and $\text{F}$ are both Bengali and speak only that language
- $\text{C},$ a Gujarati, also speaks Tamil.
- $\text{D}$ and $\text{G}$ are Tamilians and speak only Tamil.
- $\text{E}$, a Gujarati, also speaks Bengali.
- Bengalis and Tamilians refuse to share their rooms with each other.
Further, it is necessary for each participant in a room to be able to converse with at least one other participant in the same room, in at least one language.
If another participant, $\text{H},$ is to join the group, then he can be placed with any of the following, except
- $\text{B, E}$ and $\text{F}$, if $\text{H}$ is a Bengali
- $\text{C, D}$ and $\text{G},$ if $\text{H}$ is a Tamilian
- $\text{B, E}$ and $\text{F},$ if $\text{H}$ is a Tamilian
- $\text{A, B}$ and $\text{F},$ if $\text{H}$ is a Gujarati